A general and fast convergent bandwidth selection method of kernel estimator

Abstract

A new method of bandwidth estimation is developed in this article. It has the attractive property of controlled rate of convergence, regardless of sample size. This approach is applied in different contexts of functional estimation leading to bandwidth selectors that enjoy minimal assumptions, are easy to compute and have fast orders of convergence. The method is presented to jointly apply to the density, its derivatives and the distribution functions, all in one setting, and is used then to deliver bandwidth selectors in estimating density derivative functionals.

Keywords:

• Bandwidth selection
• M-estimation
• Nonparametric functional estimation
• Rate of convergence
• U-statistics